Finite Group Databasebeta

C2×#21426580 #28747072

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

Aliases

direct productC2×#21426580

Splittings

SylowC59 ⋊ C2×#2296

Subgroups

subgroupG/H
centerC23×C4C22×D59
commutatorC22×C59C24×C4
FrattiniC23C24×D59
FittingC22×#117×C59C2
socleC24×C59C24
prime radicalC25×C59C23
cosocleC23×C59C25
hypercenterC22×#117D59
hypocenterC59C2×#2296
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C23×C4 ◁ C22×#117

3854 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

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, 327951);