Finite Group Databasebeta

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#41×(C2×D43)⋊C4 #25255796

order11008
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct product#41×(C2×D43)⋊C4

Splittings

FittingC2×C4×#41×C43 ⋊ C2
SylowC43 ⋊ C22⋊C4×#41

Subgroups

subgroupG/H
centerC22×C4C23×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC2×C4×#41×C43C2
socle, cosocleC23×C43C25
prime radicalC22×#41×D43C2
hypercenterC2×C4×#41D43
hypocenterC43C22⋊C4×#41
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×C4×#41

5646 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1780 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 328767);