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D4×Q8×C239 #29504453

order15296
nilpotency class2
automorphism?
homologyAbelianization (H1) = C24×C239 · Schur multiplier (H2) = C25

Aliases

direct productD4×Q8×C239

Subgroups

subgroupG/H
center, socleC22×C239C24
commutator, Frattini, cosocleC22C24×C239
prime radicalC2×D4×C239C22
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C239 ◁ G

280 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7648

Conjugacy classes & character table

5975 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#44483651, #44483713, #44483797, …
maximal subgroup of#1627×C239, #1637×C239, #1649×C239, …
maximal normal subgroup of#1627×C239, #1637×C239, #1649×C239, …
maximal quotient ofQ8×C22⋊C4×C239, D4×C4⋊C4×C239, Q8×C4⋊C4×C239, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15296, 230);