Finite Group Databasebeta

C4×#20300265 #44402265

order29056
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4×#20300265

Splittings

SylowC227 ⋊ C4×C22⋊Q8

Subgroups

subgroupG/H
centerC22×C4C22×D227
commutatorC22×C227C23×C4
FrattiniC23C23×D227
FittingC4×C22⋊C4×C227C2
socle, cosocleC23×C227C24
prime radicalC24×C227C23
hypercenterC4×C22⋊C4D227
hypocenterC227C4×C22⋊Q8
LCSG ▷ C22×C227 ▷ C227
UCSC1 ◁ C22×C4 ◁ C4×C22⋊C4

656 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14528

Conjugacy classes & character table

4576 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29056, 7041);