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C3×#88190 #11928825

order1248
automorphism?
homologyAbelianization (H1) = C23×C3 · Schur multiplier (H2) = C2×C4

Aliases

direct productC3×#88190

Splittings

HallC3×C13 ⋊ #124
SylowC13 ⋊ C3×#124

Subgroups

subgroupG/H
centerC22×C3C22×D13
commutator, cosocleC22×C13C23×C3
FrattiniC22C22×C3×D13
Fitting, prime radicalC2×C3×D4×C13C2
socleC22×C3×C13C23
hypercenterC2×C3×D4D13
hypocenterC13C3×#124
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C3 ◁ C2×C3×D4

152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 624

A minimal faithful permutation representation — 3 generators on 28 points:

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

Conjugacy classes & character table

222 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1248, 937);