Finite Group Databasebeta

C2×#21432829 #29452587

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

Aliases

direct productC2×#21432829

Splittings

FittingC2×C59×#435 ⋊ C2
SylowC59 ⋊ C2×D4×M16

Subgroups

subgroupG/H
centerC22×C4C23×D59
commutatorC22×C59C24×C4
FrattiniC2×C4C24×D59
FittingC2×C59×#435C2
socleC23×C59C23×C4
prime radicalC22×D4×D59C4
cosocleC2×C4×C59C25
hypercenterC2×#435D59
hypocenterC59C2×D4×M16
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C2×#435

3218 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

1724 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1033466);