Finite Group Databasebeta

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C4⋊C4×D668 #36327041

order21376
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC4⋊C4×D668

Splittings

FittingC4×C4⋊C4×C167 ⋊ C2
SylowC167 ⋊ D4×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C23×D167
commutatorC22×C167C23×C4
FittingC4×C4⋊C4×C167C2
socle, cosocleC23×C167C24
prime radicalC22×D668C22
hypercenterC4×C4⋊C4D167
hypocenterC167D4×C4⋊C4
LCSG ▷ C22×C167 ▷ C167
UCSC1 ◁ C23 ◁ C4×C4⋊C4

776 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10688

Conjugacy classes & character table

3370 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21376, 7413);