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C23×C3⋊#1043 #72229441

order2400
isoclinismisoclinic class of C3⋊#1043
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC23×C3⋊#1043

Splittings

Fitting, socleC23×C3×C52 ⋊ C4
derived, HallC3×C52 ⋊ C23×C4
SylowC52 ⋊ C23×Dic3
SylowC3 ⋊ C23×#1043

Subgroups

subgroupG/H
center, hypercenterC23C3⋊#1043
commutator, hypocenterC3×C52C23×C4
FrattiniC1G
Fitting, socleC23×C3×C52C4
prime radicalC23×C3×C5⋊D5C2
cosocleC3×C5⋊D5C24
LCSG ▷ C3×C52
UCSC1 ◁ C23

1888 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 19
transitive degreeμt(G) = 600

A minimal faithful permutation representation — 4 generators on 19 points:

(5,6)(7,8,9)(10,11,14,12,13);(8,9)(11,12,13,14)(16,17,18,19);(3,4)(15,16,19,17,18);(1,2)

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×D4×C3⋊#1043, C23×D3×#1043, C24×C3⋊#1043, …
maximal normal subgroup ofC2×D4×C3⋊#1043, C23×D3×#1043, C24×C3⋊#1043, …
maximal quotient ofC2×D4×C3⋊#1043, C24×C3⋊#1043, C23×C3⋊(C3⋊#1043), …

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((5,6)(7,8,9)(10,11,14,12,13), (8,9)(11,12,13,14)(16,17,18,19), (3,4)(15,16,19,17,18), (1,2));