Finite Group Databasebeta

C22×(C2×D59)⋊C16 #28741353

order15104
automorphism?
homologyAbelianization (H1) = C23×C16 · Schur multiplier (H2) = C27

Aliases

direct productC22×(C2×D59)⋊C16

Splittings

FittingC23×C16×C59 ⋊ C2
SylowC59 ⋊ C22×C22⋊C16

Subgroups

subgroupG/H
centerC23×C8C2×D59
commutatorC2×C59C23×C16
FrattiniC2×C8C23×D59
FittingC23×C16×C59C2
socleC24×C59C2×C8
prime radicalC24×D59C8
cosocleC2×C8×C59C24
hypercenterC23×C16D59
hypocenterC59C22×C22⋊C16
LCSG ▷ C2×C59 ▷ C59
UCSC1 ◁ C23×C8 ◁ C23×C16

1470 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

3872 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 322232);