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C3×Dic46 #10587775

order552
isoclinismisoclinic class of Dic46
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C1

Aliases

direct productC3×Dic46
unambiguous semidirect productC23⋊(C3×Q8)

Splittings

HallC3×C23 ⋊ Q8
SylowC23 ⋊ C3×Q8

Subgroups

subgroupG/H
centerC2×C3C2×D23
commutator, cosocleC2×C23C22×C3
FrattiniC2C2×C3×D23
FittingC3×C4×C23C2
socle, prime radicalC2×C3×C23C22
hypercenterC3×C4D23
hypocenterC23C3×Q8
LCSG ▷ C2×C23 ▷ C23
UCSC1 ◁ C2×C3 ◁ C3×C4

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 34
transitive degreeμt(G) = 552

A minimal faithful permutation representation — 2 generators on 34 points:

(1,2,3)(4,5,6,7)(8,11,10,9)(12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34);(4,8,6,10)(5,9,7,11)(13,34)(14,33)(15,32)(16,31)(17,30)(18,29)(19,28)(20,27)(21,26)(22,25)(23,24)

Conjugacy classes & character table

147 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11764140, #11764142, #11764145, …
maximal normal subgroup of#11764140, #11764142, #11764145, …
maximal quotient ofC3×Dic23⋊C4, C3×C4⋊Dic23, C2×C3×Dic46, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(552, 13);