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C2×C23×#87704 #32913449

order18354
automorphism?
homologyAbelianization (H1) = C2×C3×C23 · Schur multiplier (H2) = C1

Aliases

direct productC2×C23×#87704

Splittings

Fitting, socle, HallC2×C7×C19×C23 ⋊ C3
derived, HallC7×C19 ⋊ C2×C3×C23
HallC7×C19×C23 ⋊ C2×C3
HallC2×C19×C23 ⋊ ΓL(1,𝔽8)
HallC19×C23 ⋊ C2×ΓL(1,𝔽8)
HallC2×C7×C23 ⋊ C19⋊C3
HallC2×C7×C19 ⋊ C3×C23
HallC7×C23 ⋊ C2×C19⋊C3
HallC2×C19 ⋊ ΓL(1,𝔽8)×C23
SylowC19 ⋊ C2×ΓL(1,𝔽8)×C23
HallC2×C7 ⋊ C23×C19⋊C3
SylowC7 ⋊ C2×C23×C19⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C23#87704
commutator, cosocle, hypocenterC7×C19C2×C3×C23
FrattiniC1G
Fitting, socleC2×C7×C19×C23C3
LCSG ▷ C7×C19
UCSC1 ◁ C2×C23

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6118

Conjugacy classes & character table

2162 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×C23×#87704, Dic23×#87704, C23×#13097582, …
maximal normal subgroup ofC4×C23×#87704, Dic23×#87704, C23×#13097582, …
maximal quotient ofC4×C23×#87704, C22×C23×#87704

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18354, 4);