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C4⋊C4×C7⋊C16 #13269140

order1792
automorphism?
homologyAbelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4⋊C4×C7⋊C16

Splittings

SylowC7 ⋊ C16×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC22×C8C22×D7
commutatorC2×C7C2×C4×C16
FittingC7×C8×C4⋊C4C2
socle, prime radicalC23×C7C22×C8
cosocleC22×C7×C8C23
hypercenterC8×C4⋊C4D7
hypocenterC7C16×C4⋊C4
LCSG ▷ C2×C7 ▷ C7
UCSC1 ◁ C22×C8 ◁ C8×C4⋊C4

398 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1792

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 84912);