Finite Group Databasebeta

#405×D227 #44408144

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

Aliases

direct product#405×D227

Splittings

Fitting#405×C227 ⋊ C2
SylowC227 ⋊ C2×#405

Subgroups

subgroupG/H
centerC2×C8C22×D227
commutatorC2×C227C22×C42
FrattiniC2×C4C23×D227
Fitting#405×C227C2
socleC22×C227C23×C4
prime radicalC23×D227C2×C4
cosocleC2×C4×C227C24
hypercenter#405D227
hypocenterC227C2×#405
LCSG ▷ C2×C227 ▷ C227
UCSC1 ◁ C2×C8 ◁ #405

592 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7264

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, 12920);