Finite Group Databasebeta

#41×(C2×D7)⋊C4 #13512995

order1792
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct product#41×(C2×D7)⋊C4

Splittings

FittingC2×C4×C7×#41 ⋊ C2
SylowC7 ⋊ C22⋊C4×#41

Subgroups

subgroupG/H
centerC22×C4C23×D7
commutatorC22×C7C24×C4
FrattiniC23C24×D7
FittingC2×C4×C7×#41C2
socle, cosocleC23×C7C25
prime radicalC22×D7×#41C2
hypercenterC2×C4×#41D7
hypocenterC7C22⋊C4×#41
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C22×C4 ◁ C2×C4×#41

5646 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 448

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, 328767);