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C3×(C2×D19)⋊C4 #11744857

order912
isoclinismisoclinic class of Dic38
automorphism?
homologyAbelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22

Aliases

direct productC3×(C2×D19)⋊C4

Splittings

FittingC2×C3×C4×C19 ⋊ C2
HallC3×C19 ⋊ C22⋊C4
SylowC19 ⋊ C3×C22⋊C4

Subgroups

subgroupG/H
centerC22×C3C2×D19
commutatorC2×C19C2×C3×C4
FrattiniC22C2×C3×D19
FittingC2×C3×C4×C19C2
socleC22×C3×C19C22
prime radicalC22×C3×D19C2
cosocleC22×C19C22×C3
hypercenterC2×C3×C4D19
hypocenterC19C3×C22⋊C4
LCSG ▷ C2×C19 ▷ C19
UCSC1 ◁ C22×C3 ◁ C2×C3×C4

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 30
transitive degreeμt(G) = 456

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

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

Conjugacy classes & character table

246 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#14269219, #14269220, #14269222, …
maximal normal subgroup of#14269219, #14269220, #14269222, …
maximal quotient ofC3×#10597262, C3×#10597263, C3×#10597266, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(912, 68);