Finite Group Databasebeta

C23×#14273663 #29452378

order15104
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC23×#14273663

Splittings

SylowC59 ⋊ C23×#108

Subgroups

subgroupG/H
centerC23×C4D236
commutatorC4×C59C24×C4
FrattiniC2×C4C24×D59
FittingC24×C8×C59C2
socleC24×C59C4⋊C4
prime radicalC25×C59Q8
cosocleC2×C4×C59C25
hypercenterC24×C8D59
hypocenterC59C23×#108
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23×C4 ◁ C24×C4 ◁ C24×C8

2846 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

3824 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1033257);