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C3×D92 #10587777

order552
isoclinismisoclinic class of Dic46
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC3×D92
unambiguous semidirect productC4⋊(C3×D23)

Splittings

FittingC3×C4×C23 ⋊ C2
HallC3×C23 ⋊ D4
SylowC23 ⋊ C3×D4

Subgroups

subgroupG/H
centerC2×C3C2×D23
commutator, cosocleC2×C23C22×C3
FrattiniC2C2×C3×D23
FittingC3×C4×C23C2
socleC2×C3×C23C22
hypercenterC3×C4D23
hypocenterC23C3×D4
LCSG ▷ C2×C23 ▷ C23
UCSC1 ◁ C2×C3 ◁ C3×C4

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 30
transitive degreeμt(G) = 276

A minimal faithful permutation representation — 2 generators on 30 points:

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

Conjugacy classes & character table

147 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11764136, #11764137, #11764139, …
maximal normal subgroup of#11764136, #11764137, #11764139, …
maximal quotient ofC3×#67263, C3×D184, C3×Dic92, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(552, 15);