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C2×C7×D1105 #44525969

order30940
automorphism?
homologyAbelianization (H1) = C22×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×C7×D1105
unambiguous semidirect product(C2×C5)⋊(C7×D221)
unambiguous semidirect product(C2×C13)⋊(C7×D85)
unambiguous semidirect product(C2×C17)⋊(C7×D65)

Splittings

Fitting, socleC2×C5×C7×C13×C17 ⋊ C2
derived, HallC5×C13×C17 ⋊ C22×C7
HallC5×C7×C13×C17 ⋊ C22
HallC7×C13×C17 ⋊ C2×D5
HallC5×C7×C17 ⋊ C2×D13
HallC5×C7×C13 ⋊ C2×D17
HallC13×C17 ⋊ C2×C7×D5
HallC7×C17 ⋊ C2×D65
HallC7×C13 ⋊ C2×D85
HallC5×C17 ⋊ C2×C7×D13
HallC5×C13 ⋊ C2×C7×D17
HallC5×C7 ⋊ C2×D221
SylowC17 ⋊ C2×C7×D65
SylowC13 ⋊ C2×C7×D85
SylowC5 ⋊ C2×C7×D221

Subgroups

subgroupG/H
center, hypercenterC2×C7D1105
commutator, cosocle, hypocenterC5×C13×C17C22×C7
FrattiniC1G
Fitting, socleC2×C5×C7×C13×C17C2
LCSG ▷ C5×C13×C17
UCSC1 ◁ C2×C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 44
transitive degreeμt(G) = 15470

A minimal faithful permutation representation — 2 generators on 44 points:

(4,5)(6,7)(8,9,10,11,12,13,14)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42)(43,44);(1,2)(3,4,6,7,5)(15,16,18,20,22,24,26,27,25,23,21,19,17)(28,29,31,33,35,37,39,41,43,44,42,40,38,36,34,32,30)

Conjugacy classes & character table

7756 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30940, 119);