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C3×#64545 #11744969

order912
automorphism?
homologyAbelianization (H1) = C23×C3 · Schur multiplier (H2) = C22

Aliases

direct productC3×#64545

Splittings

FittingC3×Q8×C19 ⋊ C2
HallC3×C19 ⋊ #41
SylowC19 ⋊ C3×#41

Subgroups

subgroupG/H
centerC2×C3C22×D19
commutator, cosocleC2×C19C23×C3
FrattiniC2C22×C3×D19
FittingC3×Q8×C19C2
socleC2×C3×C19C23
hypercenterC3×Q8D19
hypocenterC19C3×#41
LCSG ▷ C2×C19 ▷ C19
UCSC1 ◁ C2×C3 ◁ C3×Q8

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 3 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)(23,25,26,29)(24,27,28,30);(23,24,26,28)(25,30,29,27);(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(25,29)(27,30)

Conjugacy classes & character table

165 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#14269419, #14269425, #14269431, …
maximal normal subgroup of#14269419, #14269425, #14269431, …
maximal quotient ofC3×#10597336, C3×#10597338, C3×#10597339, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(912, 180);