Finite Group Databasebeta

C2×#21422176 #28503536

order15104
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C24

Aliases

direct productC2×#21422176

Splittings

SylowC59 ⋊ C2×#1375

Subgroups

subgroupG/H
centerC22×C4C4×Dic59
commutatorC4×C59C2×C4×C8
FrattiniC22×C8C22×D59
FittingC22×#97×C59C2
socleC23×C59#97
prime radicalC24×C59M16
cosocleC22×C8×C59C23
hypercenterC22×#97D59
hypocenterC59C2×#1375
LCSG ▷ C4×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C22×#97

630 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

2408 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 84415);