Finite Group Databasebeta

← Prev (#32912654) Next (#32912656) →

C4×C22⋊D571 #32912655

order18272
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC4×C22⋊D571

Splittings

FittingC22×C4×C571 ⋊ C2
SylowC571 ⋊ C4×D4

Subgroups

subgroupG/H
centerC2×C4C2×D571
commutatorC2×C571C22×C4
FrattiniC22C22×D571
FittingC22×C4×C571C2
socle, cosocleC22×C571C23
prime radicalC2×C22⋊D571C2
hypercenterC22×C4D571
hypocenterC571C4×D4
LCSG ▷ C2×C571 ▷ C571
UCSC1 ◁ C2×C4 ◁ C22×C4

94 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9136

Conjugacy classes & character table

4580 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of(C22⋊D571)⋊C8, C8×C22⋊D571, #49142334, …
maximal normal subgroup of(C22⋊D571)⋊C8, C8×C22⋊D571, #49142334, …
maximal quotient ofC4×C22⋊Dic571, C4×(C2×D571)⋊C4, C4×Dic571⋊C4, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18272, 107);