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C2×C3×#16838450 #37525470

order22932
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3×#16838450

Splittings

Fitting, socleC2×C3×C72×C13 ⋊ C2×C3
derived, HallC72×C13 ⋊ C22×C32
HallC3×C13×#3861 ⋊ C22
HallC2×C7⋊D91 ⋊ C32
HallC3×#3861 ⋊ C2×D13
SylowC72 ⋊ C2×C32×D13
SylowC13 ⋊ C2×C3×#64424

Subgroups

subgroupG/H
center, hypercenterC2×C3#16838450
commutator, cosocle, hypocenterC72×C13C22×C32
FrattiniC1G
Fitting, socleC2×C3×C72×C13C2×C3
LCSG ▷ C72×C13
UCSC1 ◁ C2×C3

600 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 3822

A minimal faithful permutation representation — 3 generators on 32 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(15,18,19,16,17,20)(22,25,26,23,24,27);(1,2,4,6,8,10,12,13,11,9,7,5,3)(21,22,24,27,26,25,23)(28,29,30)(31,32);(14,15,17,20,19,18,16)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22932, 1415);