Finite Group Databasebeta

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C4×C32×D43 #25016765

order11008
isoclinismisoclinic class of D43
automorphism?
homologyAbelianization (H1) = C2×C4×C32 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4×C32×D43

Splittings

FittingC4×C32×C43 ⋊ C2
derived, SylowC43 ⋊ C2×C4×C32

Subgroups

subgroupG/H
center, hypercenterC4×C32D43
commutator, hypocenterC43C2×C4×C32
FrattiniC2×C16C22×D43
FittingC4×C32×C43C2
socleC22×C43C22×C16
prime radicalC22×D43C2×C16
cosocleC2×C16×C43C23
LCSG ▷ C43
UCSC1 ◁ C4×C32

270 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 171 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Conjugacy classes & character table

2944 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 89736);