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D4×Q8×C277 #31799683

order17728
nilpotency class2
automorphism?
homologyAbelianization (H1) = C24×C277 · Schur multiplier (H2) = C25

Aliases

direct productD4×Q8×C277

Subgroups

subgroupG/H
center, socleC22×C277C24
commutator, Frattini, cosocleC22C24×C277
prime radicalC2×D4×C277C22
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C277 ◁ G

280 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8864

Conjugacy classes & character table

6925 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#47982270, #47982332, #47982416, …
maximal subgroup of#1627×C277, #1637×C277, #1649×C277, …
maximal normal subgroup of#1627×C277, #1637×C277, #1649×C277, …
maximal quotient ofQ8×C22⋊C4×C277, D4×C4⋊C4×C277, Q8×C4⋊C4×C277, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17728, 230);