Finite Group Databasebeta

C2×#28408986 #44408145

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

Aliases

direct productC2×#28408986

Splittings

FittingC2×C4×C8×C227 ⋊ C2
SylowC227 ⋊ C2×#405

Subgroups

subgroupG/H
centerC22×C8C2×D227
commutatorC2×C227C22×C42
FrattiniC2×C4C23×D227
FittingC2×C4×C8×C227C2
socleC23×C227C22×C4
prime radicalC23×D227C2×C4
cosocleC2×C4×C227C24
hypercenterC2×C4×C8D227
hypocenterC227C2×#405
LCSG ▷ C2×C227 ▷ C227
UCSC1 ◁ C22×C8 ◁ C2×C4×C8

592 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14528

Conjugacy classes & character table

7312 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29056, 12921);