Finite Group Databasebeta

C2×C4×C4⋊Dic271 #46838699

order34688
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×C4×C4⋊Dic271

Splittings

SylowC271 ⋊ C2×C4×C4⋊C4

Subgroups

subgroupG/H
centerC23×C4C2×D271
commutatorC2×C271C22×C42
FrattiniC23C23×D271
FittingC22×C42×C271C2
socle, prime radicalC24×C271C23
cosocleC23×C271C24
hypercenterC22×C42D271
hypocenterC271C2×C4×C4⋊C4
LCSG ▷ C2×C271 ▷ C271
UCSC1 ◁ C23×C4 ◁ C22×C42

928 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 34688

Conjugacy classes & character table

8720 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34688, 6845);