Finite Group Databasebeta

C4×#20300198 #44399418

order29056
automorphism?
homologyAbelianization (H1) = C43 · Schur multiplier (H2) = C2×C42

Aliases

direct productC4×#20300198

Splittings

SylowC227 ⋊ C4×#97

Subgroups

subgroupG/H
centerC2×C42C2×D227
commutatorC2×C227C43
FrattiniC22×C4C22×D227
FittingC2×C4×C8×C227C2
socle, prime radicalC23×C227C22×C4
cosocleC22×C4×C227C23
hypercenterC2×C4×C8D227
hypocenterC227C4×#97
LCSG ▷ C2×C227 ▷ C227
UCSC1 ◁ C2×C42 ◁ C2×C4×C8

360 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, 4194);