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C3×C4⋊#595 #11717840

order816
isoclinismisoclinic class of #63243
automorphism?
homologyAbelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2

Aliases

direct productC3×C4⋊#595
unambiguous semidirect productC4⋊(C3×#595)

Splittings

FittingC3×C4×C17 ⋊ C4
HallC3×C17 ⋊ C4⋊C4
SylowC17 ⋊ C3×C4⋊C4

Subgroups

subgroupG/H
centerC2×C3C2×#595
commutatorC2×C17C2×C3×C4
FrattiniC2C2×C3×#595
FittingC3×C4×C17C4
socleC2×C3×C17C2×C4
prime radicalC2×C3×D17C22
cosocleC2×D17C22×C3
hypercenterC3×C4#595
hypocenterC17C3×C4⋊C4
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C3 ◁ C3×C4

52 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 204

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

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

Conjugacy classes & character table

78 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#13108888, #13108890, #13108896, …
maximal normal subgroup of#13108888, #13108890, #13108896, …
maximal quotient ofC3×#10587533, C3×#10587534, C3×#10587535, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(816, 110);