Finite Group Databasebeta

C4×#16837461 #28586834

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

Aliases

direct productC4×#16837461

Splittings

FittingC42×C8×C59 ⋊ C2
SylowC59 ⋊ C4×#433

Subgroups

subgroupG/H
centerC2×C42C22×D59
commutatorC22×C59C22×C42
FrattiniC22×C4C23×D59
FittingC42×C8×C59C2
socleC23×C59C23×C4
prime radicalC23×D59C22×C4
cosocleC22×C4×C59C24
hypercenterC42×C8D59
hypocenterC59C4×#433
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C2×C42 ◁ C42×C8

970 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, 167713);