Finite Group Databasebeta

C2×C4×#14273706 #28747139

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

Aliases

direct productC2×C4×#14273706

Splittings

SylowC59 ⋊ C2×C4×C22⋊Q8

Subgroups

subgroupG/H
centerC23×C4C22×D59
commutatorC22×C59C24×C4
FrattiniC23C24×D59
FittingC23×C42×C59C2
socleC24×C59C24
prime radicalC25×C59C23
cosocleC23×C59C25
hypercenterC23×C42D59
hypocenterC59C2×C4×C22⋊Q8
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C23×C4 ◁ C23×C42

3854 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, 328018);