Finite Group Databasebeta

C2×#28408794 #44399447

order29056
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C25

Aliases

direct productC2×#28408794

Splittings

SylowC227 ⋊ C2×#340

Subgroups

subgroupG/H
centerC24C22⋊D227
commutatorC4×C227C2×C42
FrattiniC22×C4C22×D227
FittingC22×C4⋊C4×C227C2
socle, prime radicalC24×C227D4
cosocleC22×C4×C227C23
hypercenterC22×C4⋊C4D227
hypocenterC227C2×#340
LCSG ▷ C4×C227 ▷ C2×C227 ▷ C227
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×C4⋊C4

512 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 29056

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, 4223);