Finite Group Databasebeta

C2×#28408787 #44399425

order29056
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×#28408787

Splittings

SylowC227 ⋊ C2×#336

Subgroups

subgroupG/H
centerC23×C4C2×D227
commutatorC2×C227C2×C4×C8
FrattiniC22×C4C22×D227
FittingC22×C42×C227C2
socle, prime radicalC24×C227C2×C4
cosocleC22×C4×C227C23
hypercenterC22×C42D227
hypocenterC227C2×#336
LCSG ▷ C2×C227 ▷ C227
UCSC1 ◁ C23×C4 ◁ C22×C42

528 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, 4201);