Finite Group Databasebeta

C2×#21432514 #29452087

order15104
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×#21432514

Splittings

SylowC59 ⋊ C2×#2873

Subgroups

subgroupG/H
centerC22×C4C23×D59
commutatorC2×C59C23×C42
FrattiniC2×C4C24×D59
FittingC23×M16×C59C2
socleC23×C59C23×C4
prime radicalC25×C59C2×C4
cosocleC2×C4×C59C25
hypercenterC23×M16D59
hypocenterC59C2×#2873
LCSG ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C23×M16

3342 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

2456 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1032966);