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D4×#11929639 #23778860

order10144
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productD4×#11929639

Splittings

FittingD4×C317 ⋊ C4
SylowC317 ⋊ C4×D4

Subgroups

subgroupG/H
center, FrattiniC2C22×#11929639
commutator, socleC2×C317C22×C4
FittingD4×C317C4
prime radicalD4×D317C2
cosocleC2×D317C23
hypercenterD4#11929639
hypocenterC317C4×D4
LCSG ▷ C2×C317 ▷ C317
UCSC1 ◁ C2 ◁ D4

94 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

415 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD8×#11929639, SD16×#11929639, #35204262, …
maximal normal subgroup ofD8×#11929639, SD16×#11929639, #35204262, …
maximal quotient ofC22⋊C4×#11929639, C4⋊C4×#11929639, #35204170, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10144, 226);