Finite Group Databasebeta

C23×#14556119 #32904119

order18176
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C213

Aliases

direct productC23×#14556119

Splittings

SylowC71 ⋊ C23×#125

Subgroups

subgroupG/H
centerC25C22×D71
commutator, cosocleC22×C71C26
FrattiniC22C25×D71
FittingC23×C4⋊C4×C71C2
socle, prime radicalC25×C71C23
hypercenterC23×C4⋊C4D71
hypocenterC71C23×#125
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C25 ◁ C23×C4⋊C4

8414 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18176

Conjugacy classes & character table

2912 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 1076235);