Finite Group Databasebeta

C2×#21423907 #28586406

order15104
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×#21423907

Splittings

FittingC2×C59×#376 ⋊ C2
SylowC59 ⋊ C2×#1759

Subgroups

subgroupG/H
centerC22×C4C2×D236
commutatorC4×C59C22×C42
FrattiniC22×C4C23×D59
FittingC2×C59×#376C2
socleC23×C59C2×C22⋊C4
prime radicalC22×#11745685C22
cosocleC22×C4×C59C24
hypercenterC2×#376D59
hypocenterC59C2×#1759
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×#376

1662 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, 167285);