Finite Group Databasebeta

C2×M16×C22⋊D59 #29452588

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

Aliases

direct productC2×M16×C22⋊D59

Splittings

FittingC23×M16×C59 ⋊ C2
SylowC59 ⋊ C2×D4×M16

Subgroups

subgroupG/H
centerC22×C4C23×D59
commutatorC22×C59C24×C4
FrattiniC2×C4C24×D59
FittingC23×M16×C59C2
socleC23×C59C23×C4
prime radicalC23×C22⋊D59C4
cosocleC2×C4×C59C25
hypercenterC23×M16D59
hypocenterC59C2×D4×M16
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C23×M16

3218 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

2420 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1033467);