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C2×#11762565 #14528484

order2176
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4

Aliases

direct productC2×#11762565

Splittings

SylowC17 ⋊ C2×H(3,ℤ/4)

Subgroups

subgroupG/H
centerC2×C4C4×Dic17
commutatorC4×C17C2×C42
FrattiniC22×C4C22×D17
FittingC2×C17×#117C2
socleC22×C17#95
prime radicalC24×C17D4
cosocleC22×C4×C17C23
hypercenterC2×#117D17
hypocenterC17C2×H(3,ℤ/4)
LCSG ▷ C4×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×#117

404 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

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

Relationships

maximal subgroup ofH(3,ℤ/4)×Dic17, C4×#11762565, #16939492, …
maximal normal subgroup ofH(3,ℤ/4)×Dic17, C4×#11762565, #16939492, …
maximal quotient ofC2×#14526612, C2×#14526613, #16923722, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 4210);