Finite Group Databasebeta

← Prev (#26011953) Next (#26011955) →

C4×Q8×D173 #26011954

order11072
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4×Q8×D173

Splittings

FittingC4×Q8×C173 ⋊ C2
SylowC173 ⋊ C2×C4×Q8

Subgroups

subgroupG/H
centerC2×C4C22×D173
commutatorC2×C173C23×C4
FrattiniC22C23×D173
FittingC4×Q8×C173C2
socle, cosocleC22×C173C24
prime radicalC22×D173C23
hypercenterC4×Q8D173
hypocenterC173C2×C4×Q8
LCSG ▷ C2×C173 ▷ C173
UCSC1 ◁ C2×C4 ◁ C4×Q8

298 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1760 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofQ8⋊C8×D173, #36351956, #36351990, …
maximal normal subgroup ofQ8⋊C8×D173, #36351956, #36351990, …
maximal quotient ofC4×C4⋊C4×D173, C4×#19149644, C4×Q8×Dic173, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11072, 1012);