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C2×C3×C29⋊((C5⋊D5)⋊C3) #39908070

order26100
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3×C5

Aliases

direct productC2×C3×C29⋊((C5⋊D5)⋊C3)
unambiguous semidirect product(C2×C29)⋊(C3×(C5⋊D5)⋊C3)
unambiguous semidirect product(C2×C5⋊D145)⋊C32
unambiguous semidirect product(C2×C3×C5⋊D145)⋊C3

Splittings

Fitting, socleC2×C3×C52×C29 ⋊ C2×C3
derived, HallC52×C29 ⋊ C22×C32
HallC3×C29×C52⋊C3 ⋊ C22
HallC2×C5⋊D145 ⋊ C32
HallC3×C52⋊C3 ⋊ C2×D29
SylowC29 ⋊ C2×C3×(C5⋊D5)⋊C3
SylowC52 ⋊ C2×C32×D29

Subgroups

subgroupG/H
center, hypercenterC2×C3C29⋊((C5⋊D5)⋊C3)
commutator, cosocle, hypocenterC52×C29C22×C32
FrattiniC1G
Fitting, socleC2×C3×C52×C29C2×C3
LCSG ▷ C52×C29
UCSC1 ◁ C2×C3

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 49
transitive degreeμt(G) = 2610

A minimal faithful permutation representation — 2 generators on 49 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31,33)(32,42,38,35,36,44)(34,39,43,40,41,37);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(30,32,37,43,35)(31,34,36,42,40)(33,38,39,41,44)(45,46,47)(48,49)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26100, 304);