Finite Group Databasebeta

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C4⋊C4×D137 #17984041

order4384
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC4⋊C4×D137

Splittings

FittingC4⋊C4×C137 ⋊ C2
SylowC137 ⋊ C2×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC22C22×D137
commutatorC2×C137C22×C4
FittingC4⋊C4×C137C2
socle, cosocleC22×C137C23
prime radicalC22×D137C22
hypercenterC4⋊C4D137
hypocenterC137C2×C4⋊C4
LCSG ▷ C2×C137 ▷ C137
UCSC1 ◁ C22 ◁ C4⋊C4

92 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2192

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4384, 99);