Finite Group Databasebeta

C2×C4⋊C8×D271 #46844913

order34688
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC2×C4⋊C8×D271

Splittings

FittingC2×C4⋊C8×C271 ⋊ C2
SylowC271 ⋊ C22×C4⋊C8

Subgroups

subgroupG/H
centerC22×C4C22×D271
commutatorC2×C271C23×C8
FrattiniC2×C4C23×D271
FittingC2×C4⋊C8×C271C2
socleC23×C271C22×C4
prime radicalC23×D271C2×C4
cosocleC2×C4×C271C24
hypercenterC2×C4⋊C8D271
hypocenterC271C22×C4⋊C8
LCSG ▷ C2×C271 ▷ C271
UCSC1 ◁ C22×C4 ◁ C2×C4⋊C8

640 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17344

Conjugacy classes & character table

5480 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34688, 13059);