Finite Group Databasebeta

C22×#20300199 #44408138

order29056
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26

Aliases

direct productC22×#20300199

Splittings

SylowC227 ⋊ C22×#97

Subgroups

subgroupG/H
centerC23×C4C2×D227
commutatorC2×C227C22×C42
FrattiniC2×C4C23×D227
FittingC22×C42×C227C2
socle, prime radicalC24×C227C2×C4
cosocleC2×C4×C227C24
hypercenterC22×C42D227
hypocenterC227C22×#97
LCSG ▷ C2×C227 ▷ C227
UCSC1 ◁ C23×C4 ◁ C22×C42

680 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 29056

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, 12914);