Finite Group Databasebeta

C2×C4×#14273650 #28586436

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

Aliases

direct productC2×C4×#14273650

Splittings

SylowC59 ⋊ C2×C4×#103

Subgroups

subgroupG/H
centerC23×C4C22⋊D59
commutatorC4×C59C22×C42
FrattiniC22×C4C23×D59
FittingC2×C4×C4⋊C4×C59C2
socle, prime radicalC24×C59C2×D4
cosocleC22×C4×C59C24
hypercenterC2×C4×C4⋊C4D59
hypocenterC59C2×C4×#103
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23×C4 ◁ C22×C42 ◁ C2×C4×C4⋊C4

1726 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15104

Conjugacy classes & character table

2432 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 167315);