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D4×#1057 #11719143

order832
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23

Aliases

direct productD4×#1057

Splittings

SylowC13 ⋊ C8×D4

Subgroups

subgroupG/H
center, FrattiniC22C22×#261
commutatorC2×C13C22×C8
Fitting, prime radicalC2×D4×C13C4
socleC22×C13C22×C4
cosocleC2×Dic13C23
hypercenterC2×D4#261
hypocenterC13C8×D4
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×D4

134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

70 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD8×#1057, #13130416, SD16×#1057, …
maximal normal subgroup ofD8×#1057, #13130416, SD16×#1057, …
maximal quotient ofD8×#1057, SD16×#1057, Q16×#1057, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(832, 1109);