Finite Group Databasebeta

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C22⋊C4×#10597845 #23758211

order10048
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4

Aliases

direct productC22⋊C4×#10597845

Splittings

FittingC22⋊C4×C157 ⋊ C4
SylowC157 ⋊ C4×C22⋊C4

Subgroups

subgroupG/H
center, FrattiniC22C22×#10597845
commutatorC2×C157C2×C42
FittingC22⋊C4×C157C4
socleC22×C157C22×C4
prime radicalC23×D157C22
cosocleC22×D157C23
hypercenterC22⋊C4#10597845
hypocenterC157C4×C22⋊C4
LCSG ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22⋊C4

258 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 84 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

430 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#99×#10597845, C2×C22⋊C4×#10597845, #117×#10597845, …
maximal normal subgroup of#99×#10597845, C2×C22⋊C4×#10597845, #117×#10597845, …
maximal quotient of#95×#10597845, #34115309, #34115311, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10048, 1487);