Finite Group Databasebeta

C4×#16837384 #28586367

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

Aliases

direct productC4×#16837384

Splittings

FittingC2×C4×M16×C59 ⋊ C2
SylowC59 ⋊ C4×#413

Subgroups

subgroupG/H
centerC42(C2×D59)⋊C4
commutatorC22×C59C22×C42
FrattiniC22×C4C23×D59
FittingC2×C4×M16×C59C2
socleC22×C59C22×C22⋊C4
prime radicalC22×#11745685C22
cosocleC22×C4×C59C24
hypercenterC2×C4×M16D59
hypocenterC59C4×#413
LCSG ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C42 ◁ C22×C42 ◁ C2×C4×M16

1570 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, 167246);