Finite Group Databasebeta

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C22×(C22⋊D271)⋊C4 #46849532

order34688
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC22×(C22⋊D271)⋊C4

Splittings

FittingC22×C22⋊C4×C271 ⋊ C2
SylowC271 ⋊ C22×C4×D4

Subgroups

subgroupG/H
centerC24C22×D271
commutatorC2×C271C24×C4
FrattiniC22C24×D271
FittingC22×C22⋊C4×C271C2
socleC24×C271C23
prime radicalC23×C22⋊D271C2
cosocleC22×C271C25
hypercenterC22×C22⋊C4D271
hypocenterC271C22×C4×D4
LCSG ▷ C2×C271 ▷ C271
UCSC1 ◁ C24 ◁ C22×C22⋊C4

2528 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, 17678);