Finite Group Databasebeta

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C2×C4×C4⋊Dic173 #36355898

order22144
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×C4×C4⋊Dic173

Splittings

SylowC173 ⋊ C2×C4×C4⋊C4

Subgroups

subgroupG/H
centerC23×C4C2×D173
commutatorC2×C173C22×C42
FrattiniC23C23×D173
FittingC22×C42×C173C2
socle, prime radicalC24×C173C23
cosocleC23×C173C24
hypercenterC22×C42D173
hypocenterC173C2×C4×C4⋊C4
LCSG ▷ C2×C173 ▷ C173
UCSC1 ◁ C23×C4 ◁ C22×C42

928 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 22144

Conjugacy classes & character table

5584 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22144, 6845);