Finite Group Databasebeta

C22×C4×C8×D59 #29452067

order15104
automorphism?
homologyAbelianization (H1) = C23×C4×C8 · Schur multiplier (H2) = C29×C4

Aliases

direct productC22×C4×C8×D59

Splittings

FittingC22×C4×C8×C59 ⋊ C2
derived, SylowC59 ⋊ C23×C4×C8

Subgroups

subgroupG/H
center, hypercenterC22×C4×C8D59
commutator, hypocenterC59C23×C4×C8
FrattiniC2×C4C24×D59
FittingC22×C4×C8×C59C2
socleC24×C59C22×C4
prime radicalC24×D59C2×C4
cosocleC2×C4×C59C25
LCSG ▷ C59
UCSC1 ◁ C22×C4×C8

4638 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

3968 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1032946);