Finite Group Databasebeta

#25017123

order11008
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C4

Aliases

No aliases for this group.

Splittings

SylowC43 ⋊ #13639

Subgroups

subgroupG/H
centerC4×C16C2×D43
commutatorC2×C43C22×C32
FrattiniC2×C16C22×D43
FittingC2×C4×C16×C43C2
socleC22×C43C22×C16
prime radicalC23×C43C2×C16
cosocleC2×C16×C43C23
hypercenterC2×C4×C16D43
hypocenterC43#13639
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C4×C16 ◁ C2×C4×C16

202 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^8,43|a^2=e,c^2=d,e^2=f,f^2=g,g^2=h,b^a=bd,i^a=i^42

Conjugacy classes & character table

2848 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 90094);