Finite Group Databasebeta

C2×D4×C227⋊C8 #44408407

order29056
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC2×D4×C227⋊C8

Splittings

SylowC227 ⋊ C2×C8×D4

Subgroups

subgroupG/H
centerC22×C4C22×D227
commutatorC2×C227C23×C8
FrattiniC2×C4C23×D227
FittingC2×C4×D4×C227C2
socleC23×C227C22×C4
prime radicalC22×D4×C227C4
cosocleC2×C4×C227C24
hypercenterC2×C4×D4D227
hypocenterC227C2×C8×D4
LCSG ▷ C2×C227 ▷ C227
UCSC1 ◁ C22×C4 ◁ C2×C4×D4

616 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14528

Conjugacy classes & character table

4600 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29056, 13183);