Finite Group Databasebeta

← Prev (#19143355) Next (#19143357) →

C4×Q16×D43 #19143356

order5504
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4×Q16×D43

Splittings

FittingC4×Q16×C43 ⋊ C2
SylowC43 ⋊ C2×C4×Q16

Subgroups

subgroupG/H
centerC2×C4D4×D43
commutatorC4×C43C23×C4
FrattiniC2×C4C23×D43
FittingC4×Q16×C43C2
socleC22×C43C22×D4
hypercenterC4×Q16D43
hypocenterC43C2×C4×Q16
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×Q16

488 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

644 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD43×#1332, #25006348, D43×#1334, …
maximal normal subgroup ofD43×#1332, #25006348, D43×#1334, …
maximal quotient ofC8×Q16×D43, D43×#1584, D43×#1591, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5504, 13271);