Finite Group Databasebeta

C4⋊C4×(C2×D7)⋊C4 #13275209

order1792
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4

Aliases

direct productC4⋊C4×(C2×D7)⋊C4

Splittings

FittingC2×C4×C7×C4⋊C4 ⋊ C2
SylowC7 ⋊ C22⋊C4×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC24C23×D7
commutatorC22×C7C22×C42
FittingC2×C4×C7×C4⋊C4C2
socle, cosocleC24×C7C24
prime radicalC24×D7C23
hypercenterC2×C4×C4⋊C4D7
hypocenterC7C22⋊C4×C4⋊C4
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

2574 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 896

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 90981);