Finite Group Databasebeta

C22⋊C16×Dic59 #28503718

order15104
automorphism?
homologyAbelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C23×C4

Aliases

direct productC22⋊C16×Dic59

Splittings

SylowC59 ⋊ C4×C22⋊C16

Subgroups

subgroupG/H
center, FrattiniC22×C8C22×D59
commutatorC2×C59C2×C4×C16
FittingC2×C59×C22⋊C16C2
socleC23×C59C22×C8
prime radicalC24×C59C2×C8
cosocleC22×C8×C59C23
hypercenterC2×C22⋊C16D59
hypocenterC59C4×C22⋊C16
LCSG ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C8 ◁ C2×C22⋊C16

614 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

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, 84597);