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C2×C3×C5×C7×D31 #27189285

order13020
isoclinismisoclinic class of D31
automorphism?
homologyAbelianization (H1) = C22×C3×C5×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C5×C7×D31

Splittings

Fitting, socleC2×C3×C5×C7×C31 ⋊ C2
derived, SylowC31 ⋊ C22×C3×C5×C7
HallC3×C5×C7×C31 ⋊ C22
HallC5×C7×C31 ⋊ C22×C3
HallC3×C7×C31 ⋊ C22×C5
HallC3×C5×C31 ⋊ C22×C7
HallC7×C31 ⋊ C22×C3×C5
HallC5×C31 ⋊ C22×C3×C7
HallC3×C31 ⋊ C22×C5×C7

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C7D31
commutator, cosocle, hypocenterC31C22×C3×C5×C7
FrattiniC1G
Fitting, socleC2×C3×C5×C7×C31C2
LCSG ▷ C31
UCSC1 ◁ C2×C3×C5×C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 48
transitive degreeμt(G) = 6510

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

Conjugacy classes & character table

3570 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13020, 252);