Finite Group Databasebeta

C2×#28408807 #44401323

order29056
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23

Aliases

direct productC2×#28408807

Splittings

SylowC227 ⋊ C2×#346

Subgroups

subgroupG/H
centerC22×C8C2×D227
commutatorC2×C227C2×C4×C8
FrattiniC2×C8C22×D227
FittingC22×C16×C227C2
socle, prime radicalC23×C227C2×C8
cosocleC2×C8×C227C23
hypercenterC22×C16D227
hypocenterC227C2×#346
LCSG ▷ C2×C227 ▷ C227
UCSC1 ◁ C22×C8 ◁ C22×C16

200 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, 6099);