Finite Group Databasebeta

C2×#21425854 #28741671

order15104
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×#21425854

Splittings

SylowC59 ⋊ C2×#2151

Subgroups

subgroupG/H
centerC22×C8C22×D59
commutatorC22×C59C23×C8
FrattiniC2×C8C23×D59
FittingC23×C16×C59C2
socleC23×C59C22×C8
prime radicalC24×C59C2×C8
cosocleC2×C8×C59C24
hypercenterC23×C16D59
hypocenterC59C2×#2151
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C22×C8 ◁ C23×C16

734 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, 322550);