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C32×#63118 #14556802

order2340
isoclinismisoclinic class of #63118
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C3

Aliases

direct productC32×#63118

Splittings

Fitting, socle, HallC32×C5×C13 ⋊ C4
derived, HallC5×C13 ⋊ C32×C4
HallC32×C13 ⋊ Dic5
HallC32×C5 ⋊ #261
SylowC13 ⋊ C32×Dic5
SylowC5 ⋊ C32×#261

Subgroups

subgroupG/H
center, hypercenterC32#63118
commutator, hypocenterC5×C13C32×C4
FrattiniC1G
Fitting, socleC32×C5×C13C4
prime radicalC32×C5×D13C2
cosocleC5×D13C2×C32
LCSG ▷ C5×C13
UCSC1 ◁ C32

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 585

A minimal faithful permutation representation — 2 generators on 24 points:

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

Conjugacy classes & character table

207 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC32×#13049904, C32×C5×#63118, C32×#13049935, …
maximal normal subgroup ofC32×C5×#63118, C32×C7×#63118, C32×C11×#63118, …
maximal quotient ofC32×#13049904, C32×C5×#63118, C32×#13049935, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2340, 106);