Finite Group Databasebeta

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C22×(C22⋊D167)⋊C4 #36337306

order21376
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC22×(C22⋊D167)⋊C4

Splittings

FittingC22×C22⋊C4×C167 ⋊ C2
SylowC167 ⋊ C22×C4×D4

Subgroups

subgroupG/H
centerC24C22×D167
commutatorC2×C167C24×C4
FrattiniC22C24×D167
FittingC22×C22⋊C4×C167C2
socleC24×C167C23
prime radicalC23×C22⋊D167C2
cosocleC22×C167C25
hypercenterC22×C22⋊C4D167
hypocenterC167C22×C4×D4
LCSG ▷ C2×C167 ▷ C167
UCSC1 ◁ C24 ◁ C22×C22⋊C4

2528 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10688

Conjugacy classes & character table

3400 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21376, 17678);