Finite Group Databasebeta

C2×D4×#11745664 #29452591

order15104
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×D4×#11745664

Splittings

SylowC59 ⋊ C2×D4×M16

Subgroups

subgroupG/H
centerC22×C4C23×D59
commutatorC22×C59C24×C4
FrattiniC2×C4C24×D59
FittingC22×C4×D4×C59C2
socleC23×C59C23×C4
prime radicalC23×D4×C59C4
cosocleC2×C4×C59C25
hypercenterC22×C4×D4D59
hypocenterC59C2×D4×M16
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C22×C4×D4

3218 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

2420 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1033470);