Finite Group Databasebeta

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C4×C4⋊C4×D271 #46838697

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

Aliases

direct productC4×C4⋊C4×D271

Splittings

FittingC4×C4⋊C4×C271 ⋊ C2
SylowC271 ⋊ C2×C4×C4⋊C4

Subgroups

subgroupG/H
centerC22×C4C22×D271
commutatorC2×C271C22×C42
FrattiniC23C23×D271
FittingC4×C4⋊C4×C271C2
socle, cosocleC23×C271C24
prime radicalC23×D271C23
hypercenterC4×C4⋊C4D271
hypocenterC271C2×C4×C4⋊C4
LCSG ▷ C2×C271 ▷ C271
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

928 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, 6843);