Finite Group Databasebeta

C4×#20300296 #44408158

order29056
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC4×#20300296

Splittings

FittingC4×M16×C227 ⋊ C2
SylowC227 ⋊ C4×#131

Subgroups

subgroupG/H
centerC42C22×D227
commutatorC2×C227C22×C42
FrattiniC2×C4C23×D227
FittingC4×M16×C227C2
socleC22×C227C23×C4
prime radicalC2×#16813884C22
cosocleC2×C4×C227C24
hypercenterC4×M16D227
hypocenterC227C4×#131
LCSG ▷ C2×C227 ▷ C227
UCSC1 ◁ C42 ◁ C4×M16

572 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14528

Conjugacy classes & character table

4600 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29056, 12934);