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C2×C4×C8×D227 #44408133

order29056
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×C4×C8×D227

Splittings

FittingC2×C4×C8×C227 ⋊ C2
derived, SylowC227 ⋊ C22×C4×C8

Subgroups

subgroupG/H
center, hypercenterC2×C4×C8D227
commutator, hypocenterC227C22×C4×C8
FrattiniC2×C4C23×D227
FittingC2×C4×C8×C227C2
socleC23×C227C22×C4
prime radicalC23×D227C2×C4
cosocleC2×C4×C227C24
LCSG ▷ C227
UCSC1 ◁ C2×C4×C8

760 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14528

Conjugacy classes & character table

7360 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29056, 12909);