Finite Group Databasebeta

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C23×C22⋊#1044 #72223516

order3200
isoclinismisoclinic class of #87863
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C211×C5

Aliases

direct productC23×C22⋊#1044

Splittings

FittingC25×C52 ⋊ C4
SylowC52 ⋊ C23×C22⋊C4

Subgroups

subgroupG/H
centerC24C2×#1044
commutatorC2×C52C24×C4
FrattiniC2C24×#1044
FittingC25×C52C4
socleC24×C52C2×C4
prime radicalC25×C5⋊D5C2
cosocleC2×C5⋊D5C25
hypercenterC25#1044
hypocenterC52C23×C22⋊C4
LCSG ▷ C2×C52 ▷ C52
UCSC1 ◁ C24 ◁ C25

14914 conjugacy classes of subgroups; only the 1342 normal subgroups are shown.

normal subgroups only

This group has 14914 conjugacy classes of subgroups — too many to draw. Only its 1342 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

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

Relationships

maximal quotient of#72223517

GAP

Past the SmallGroups library coverage — no SmallGroups id.