Finite Group Databasebeta

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C4⋊C4×#11924031 #34012665

order18688
automorphism?
homologyAbelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4⋊C4×#11924031

Splittings

SylowC73 ⋊ C16×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC22×C4C22×#64408
commutatorC2×C73C2×C4×C16
FittingC4×C4⋊C4×C73C4
socle, prime radicalC23×C73C22×C8
cosocleC22×#10596831C23
hypercenterC4×C4⋊C4#64408
hypocenterC73C16×C4⋊C4
LCSG ▷ C2×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

398 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18688

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 1096249);