Finite Group Databasebeta

C23×#14273651 #29452201

order15104
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC23×#14273651

Splittings

SylowC59 ⋊ C23×#103

Subgroups

subgroupG/H
centerC25C22⋊D59
commutatorC4×C59C24×C4
FrattiniC2×C4C24×D59
FittingC24×Q8×C59C2
socle, prime radicalC25×C59D4
cosocleC2×C4×C59C25
hypercenterC24×Q8D59
hypocenterC59C23×#103
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C25 ◁ C24×C4 ◁ C24×Q8

5502 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15104

Conjugacy classes & character table

2432 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1033080);