Finite Group Databasebeta

C2×#21432945 #29452814

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

Aliases

direct productC2×#21432945

Splittings

FittingC2×C59×#442 ⋊ C2
SylowC59 ⋊ C2×#2948

Subgroups

subgroupG/H
centerC23C2×D4×D59
commutatorC4×C59C24×C4
FrattiniC2×C4C24×D59
FittingC2×C59×#442C2
socleC23×C59C22×D4
prime radicalC22×D8×D59C2
cosocleC2×C4×C59C25
hypercenterC2×#442D59
hypocenterC59C2×#2948
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

3086 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

1364 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1033693);