Finite Group Databasebeta

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C2×C4⋊C4×Dic271 #46838701

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
centerC24C22×D271
commutatorC2×C271C22×C42
FrattiniC23C23×D271
FittingC22×C4⋊C4×C271C2
socle, prime radicalC24×C271C23
cosocleC23×C271C24
hypercenterC22×C4⋊C4D271
hypocenterC271C2×C4×C4⋊C4
LCSG ▷ C2×C271 ▷ C271
UCSC1 ◁ C24 ◁ C22×C4⋊C4

928 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 34688

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, 6847);