Finite Group Databasebeta

C2×C22⋊C16×D59 #28741352

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

Aliases

direct productC2×C22⋊C16×D59

Splittings

FittingC2×C59×C22⋊C16 ⋊ C2
SylowC59 ⋊ C22×C22⋊C16

Subgroups

subgroupG/H
centerC22×C8C22×D59
commutatorC2×C59C23×C16
FrattiniC2×C8C23×D59
FittingC2×C59×C22⋊C16C2
socleC23×C59C22×C8
prime radicalC24×D59C8
cosocleC2×C8×C59C24
hypercenterC2×C22⋊C16D59
hypocenterC59C22×C22⋊C16
LCSG ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C8 ◁ C2×C22⋊C16

1470 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

2480 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 322231);