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Cayley diagram

C2×#4185 #66387

order324
isoclinismisoclinic class of #4185
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×#4185

Splittings

FittingC2×#732 ⋊ C2
derived, Sylow#732 ⋊ C22

Subgroups

subgroupG/H
center, hypercenterC2#4185
commutator, cosocle, hypocenter#732C22
FrattiniC32C2×C3⋊D3
FittingC2×#732C2
socleC2×C3#272
LCSG ▷ #732
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 29
transitive degreeμt(G) = 54

A minimal faithful permutation representation — 3 generators on 29 points:

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

Conjugacy classes & character table

26 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#4185⋊C4, #10619563, #10619565, …
maximal normal subgroup of#4185⋊C4, #10619563, #10619565, …
maximal quotient of#10619666, C4×#4185, C4⋊#4185, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(324, 79);