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D4×Q8×C257 #30656418

order16448
nilpotency class2
automorphism?
homologyAbelianization (H1) = C24×C257 · Schur multiplier (H2) = C25

Aliases

direct productD4×Q8×C257

Subgroups

subgroupG/H
center, socleC22×C257C24
commutator, Frattini, cosocleC22C24×C257
prime radicalC2×D4×C257C22
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C257 ◁ G

280 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8224

Conjugacy classes & character table

6425 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#45663423, #45663485, #45663569, …
maximal subgroup of#1627×C257, #1637×C257, #1649×C257, …
maximal normal subgroup of#1627×C257, #1637×C257, #1649×C257, …
maximal quotient ofQ8×C22⋊C4×C257, D4×C4⋊C4×C257, Q8×C4⋊C4×C257, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16448, 230);